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Time series and system analysis with applications. (English) Zbl 0586.62141

New York etc.: John Wiley and Sons. XVIII, 586 p. (1983).
Engineers and scientists in system analysis use mathematical models, usually differential equations, developed from a conjectured physical mechanism. For complicated systems, an empirical approach, such as frequency analysis, is employed. On the other hand, statisticians and economists approximate their models, using difference equations, from plots of empirical autocorrelations and spectra.
If time series and system analysis are brought together, it should be possible to avoid the considerable trial and error presently needed in both fields and vastly improve their applications. In the 1973 Ph.D. dissertation of the first author, with the second author as advisor, a new philosophy of system analysis that bypasses this element of trial and error and provides models in the form of difference/differential equations directly from the observed data was outlined with the requisite mathematical foundation.
An application of this new philosophy to time series modeling yields a sequential strategy, as in regression analysis. Once the time series is considered as the response of a system, it can be modeled with increasing degrees of freedom justified by the data. Successively higher order models are fitted by least squares until the improvement in the fit is statistically insignificant.
The book is application-oriented. The new tool has been used for system identification, signature analysis, physical characterization, control, and even engineering design. Obviously, it is most useful for forecasting, which was the original purpose of the time series development. To enhance the ability for long-term forecasting, both stochastic and deterministic approaches are presented.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62P99 Applications of statistics
93E99 Stochastic systems and control
93E20 Optimal stochastic control
62N99 Survival analysis and censored data
93-02 Research exposition (monographs, survey articles) pertaining to systems and control theory